After compiling from source, 1.6.1 gets a bit further but Ubuntu still doesn't like SDL and the shaders.
I think you are right, it is either 1.53 or running the quest in Wine with the windows version of Solarus.
Anyway, this is what i get in the console.
Info: Solarus 1.6.1
Info: Opening quest '/home/me/Desktop/My Zelda Quest master'
Info: Joypad support enabled: true
Info: SDL: 2.0.8
Info: Failed to obtain core GL. Trying compatibility instead...
Info: Failed to initialize SDL shader Hack. Shaders unavailable.
Info: Renderer: SDLRenderer : software